Bohr’s Theory of the Atom: Content and Commitment

1. Bohr’s Theory of the Atom: Content and Commitment Peter Vickers, University of Leeds, phl4pv@leeds.ac.uk

2. Bohr’s Postulates • 1913 trilogy, pp.874-875 • Negatively charged electrons orbit a positively charged nucleus in a discrete number of ‘stationary states’. • Orbits maintained by Coulomb attraction. • Radiation is only emitted when an electron makes a transition between two stationary states, and such that E=hv.

3. Bohr’s Postulates • The different stationary states of a simple system consisting of an electron rotating round a positive nucleus are determined by the condition that the ratio between the total energy, emitted during the formation of the configuration, and the frequency of revolution of the electron is an entire multiple of h/2 [E=nhω/2]. Assuming that the orbit of the electron is circular, this assumption is equivalent with the assumption that the angular momentum of the electron round the nucleus is equal to an entire multiple of h/2π [M=nћ].

4. Bohr’s Postulates • The different stationary states of a simple system consisting of an electron rotating round a positive nucleus are determined by the condition that the ratio between the total energy, emitted during the formation of the configuration, and the frequency of revolution of the electron is an entire multiple of h/2 [E=nhω/2]. Assuming that the orbit of the electron is circular, this assumption is equivalent with the assumption that the angular momentum of the electron round the nucleus is equal to an entire multiple of h/2π [M=nћ].

5. Bohr’s Postulates • The different stationary states of a simple system consisting of an electron rotating round a positive nucleus are determined by the condition that the ratio between the total energy, emitted during the formation of the configuration, and the frequency of revolution of the electron is an entire multiple of h/2 [E=nhω/2]. Assuming that the orbit of the electron is circular, this assumption is equivalent with the assumption that the angular momentum of the electron round the nucleus is equal to an entire multiple of h/2π [M=nћ].

6. Bohr’s Postulates • Eisberg and Resnick, 1985 • “An electron in an atom moves in a circular orbit…” • Exclusively refer to quantized angular momentum. • No mention of restriction to ‘simple systems’. • Millikan, 1917, Kramers and Holst, 1923, Brown, 1990 and Norton, 2000.

7. The Quantum Condition p.7: ‘special assumptions’, from which follows E=nhω/2. p.12: E=f(n)hω p.15: E can stand for kinetic energy for circular orbits. p.15: Angular momentum. M=nћ p.875: E=nhω/2 for ‘simple systems’. After 1913: E stands for kinetic energy. 1915: E is average kinetic energy (simple systems). 1915/16: phase-integral quantum conditions.

8. The Quantum Condition • Many different quantum conditions • Quantum condition in the theory → Many different theories?

9. One Theory? • Use of a single term, ‘Bohr’s theory’. • Consider the term ‘Peter Vickers’.

11. One Theory? • Use of a single term, ‘Bohr’s theory’. • Consider the term ‘Peter Vickers’. • Same with Bohr’s theory?

12. One Theory? Disanalogy: • ‘Peter Vickers used to be 5 feet tall’ • ‘Peter Vickers used to be 6 feet tall’ • ‘Bohr’s theory was consistent’ (Bartelborth, 1989). • ‘Bohr’s theory was inconsistent’ (Brown, 1990).

13. Conflict? • Many different quantum conditions. • Quantum condition in the theory. • There is a single, stable thing: Bohr’s theory.

14. Rejecting the Quantum Condition • Kramers and Holst, 1923: ‘two fundamental hypotheses’ of the theory. • Heilbron and Kuhn, 1969: from December 1913 onwards Bohr proceeded “without any quantum condition at all”. • Norton, 2000: “the sole content of [E=f(n)hω] is an indexing of the energies [E] by a parameter [n].”

15. Rejecting the Quantum Condition • E=f(n)hω + Balmer formula (assumption that lines caused by transitions) → E=nhω/2 • Bohr never gives a general quantum condition • Confirmation • Acceptance

16. Rejecting the Quantum Condition • Bohr’s theory a theory of the atom. • Explains general phenomena: • J.J. Thomson’s ‘cathode rays’ • Rutherford’s α-particle scattering • Stability and neutral charge of elements • Balmer and Pickering lines specific to hydrogen and ionised helium. • E=nhω/2 part of a theory of Hydrogen and He+.

17. Conclusion • Many different quantum conditions. • Quantum condition in the theory. • There is a single, stable thing: Bohr’s theory. Belot, 2006: “[I]n choosing a sense for the term ‘theory’ in philosophy of science, we have a trade off between fidelity to common use and fecundity of the explicans.”